Since you are not looking for SOT
– Last Updated: Apr-23-10 12:24 PM EST –
specifically, you can look at the more slender under 16 foot sea kayaks. I paddle my 13.5 Perception Sonoma Airalight a lot on white water up to class III (mostly class II and class I with a couple of rapids getting into easy class III at some water levels).
These I've seen for under $600 used in great condition. I use mine for all sorts of paddling and it can keep up with moderately paced touring groups on flat water just fine.
The boat works very well for exercise, actually. It is fast (for its length) and is light (about 40lb), narrow at the catch area so it allows an efficient paddling stroke - good for fittness paddling since you mention it and to cover some distance. Occasional bumps and going over a rock here and there so far have only produced very shallow scratches so the material is OK for this.
But realistically, any 12-16 footer should do well for class I and easy class II.
You will get used to the current if you paddle a lot. So if you are OK with somewhat of a learning curve, go for something that is no wider than 24". In the currents eventually you would want to develop balance and not rely on the boat's stability and once you do that, the extra width will just be slowing you down.
EDIT: forgot to mention - your size is in the sweet spot for most kayaks and for exercise purposes, you should be looking for the ones made for small to medium paddlers. I am considered a tall and large paddler at 6'4" and 185lb (with day gear a little over 200lb) and a boat like the Sonoma is just perfect for day trips and holds my weight and size very well (foot pegs not long enough but I have custom foot rest placed; you should have no problems). Look at Tsunami 125 or 135 too. For Class I really anything should work and you can go longer than that for speed. But if there is a strong current that you do not want to fight and instead you will be addy-hopping upstream you want to stay below 16 feet probably for maneuverability.